sunflower animation

Here's a growing sunflower for you (if we're lucky). More below.

(If the animation doesn't show, here is a full-sized screen shot.)

What's a meristem?

A meristem is the tip or center of a new plant part (stem, root, leaf, flower, fruit...) where growth of the part starts and gets its pattern. It's something like a stem-cell niche in animals: a bunch of undifferentiated cells proliferate there, then become more differentiated as they either spread away from the meristem, or push the meristem ahead of themselves. Here's the Wikipedia article. Often, in flowers and leaf buds, but even at branch tips, the meristem is hidden-- there's a little indent like a whirlpool in the center that everything else has emerged / is emerging from. This applet animates the pattern of seeds in a growing sunflower. The process of the seed buds emerging and moving away from the meristem, called "spiral phylotaxis," is what produces this pattern. So I put a meristem in the center. Artist's conception.

The code

The applet was originally written for the Java-based Processing environment. On this page, the unchanged source code is being run in your browser by a script from the Processing.js project. There's also an equivalent Python version to run with PyProcessing.

More about spiral phylotaxis

The applet cheats, using the golden-ratio angle. Plants don't actually calculate the golden ratio; the pattern is formed by seeds growing into gaps between the earlier seeds, which is demonstrated brilliantly by S. Douady and Y. Couder in this video.

Vi Hart has a great series of videos, "Doodling in Math Class: Spirals, Fibonacci and Being a Plant."
Part One
Part Two
Part Three, which gets down to the nitty gritty and a bit of debunking, and
Notes and References, where the links are rectangles that appear as the video plays.

Hart references the short article "The Mathematical Lives of Plants," by Julie J. Rehmeyer (web-style version here).

--Steve Witham
Up to my home page.